Brokerage firms were once the bread and butter of Wall Street. Still, a recent conflict between Morgan Stanley and Citigroup has exposed just how hard it is for even experienced hands in the business to quantify the value of such operations.

During Morgan Stanley’s earnings call last Thursday, its chief executive, James P. Gorman, trumpeted the strengths of its brokerage unit, saying it was an important business for the bank. Yet days earlier, as part of negotiations with Citigroup, Morgan Stanley placed a surprisingly low valuation on the same unit.

That apparent inconsistency reveals how much is at stake as Morgan Stanley wrangles with Citigroup over acquiring a bigger share of the unit they jointly own, Morgan Stanley Smith Barney. The unit, formed of the union of Citigroup’s Smith Barney division and Morgan Stanley’s brokerage businesses, manages the assets of wealthy individuals and is led by Gregory J. Fleming.

Mr. Gorman has said that he wants it to play a big role in Morgan Stanley’s future.

On a conference call last Thursday, Mr. Gorman was enthusiastic about Morgan Stanley Smith Barney. “Our wealth management business will considerably increase its value to our clients and financial advisers through superior functionality, and to our shareholders through enhanced and stable earnings,” he said.

The bank bought a 51 percent stake in Morgan Stanley Smith Barney from Citigroup in 2009, and the current talks are over what it should pay for an additional 14 percent.

In a financial filing with the Securities and Exchange Commission last Thursday about the talks, Citigroup implied that Morgan Stanley had made a bid that placed the value of all of the operations of Morgan Stanley Smith Barney at about $9 billion. Citigroup says it is worth about $23 billion. Because of the distance between the assessments, both banks must now call in a third-party appraiser, the investment bank Perella Weinberg Partners.

Executives from Morgan Stanley Smith Barney will give an overview of the business to Perella Weinberg in a meeting Thursday at Morgan Stanley’s offices in Purchase, N.Y., said people who had been briefed on the talks but were not authorized to speak on the record because the discussions were private.

Officials from Citigroup and Morgan Stanley will also attend the first meeting with the appraisers, these people said. Representatives for both companies declined to comment on the meeting.

Then, next week, Citigroup and Morgan Stanley will separately make their cases to Perella Weinberg.

The difference between the banks’ valuations is probably influenced by negotiating tactics. Morgan Stanley wants to have full control over the business for as low a price as possible. Meanwhile, Citigroup probably wants it to be worth more. If it is worth less than Citigroup estimates, the bank, under accounting rules, must make a write-down on its balance sheet. That could lead to a large and possibly embarrassing charge against earnings and capital.

A valuation by Perella Weinberg that is far off both banks’ assessments could call into question the accuracy of their balance sheets.

According to a recent filing, Citigroup’s balance sheet gives Morgan Stanley Smith Barney a value of around $22 billion, which is comparable to what Citi has told Morgan Stanley it is worth.

Morgan Stanley has not stated the precise value its balance sheet places on the unit, but filings suggest it could be $10 billion to $14 billion. The upper end of that range is far from the $9 billion implied by its bid for the 14 percent stake. Citigroup may have most to lose if the appraisal is far different from its valuation.

Wall Street analysts value Morgan Stanley Smith Barney at around $15 billion. But that would be $7 billion below Citigroup’s valuation. In such a case, Citigroup would book a loss, though only on its stake, so it would be less than $3.5 billion. That would hurt some important measures of capital, but not others. Any such damage would not escape the notice of regulators, like the Federal Reserve, which in March rejected Citigroup’s request to return more capital to shareholders.

But Morgan Stanley may also face questions about its decision to emphasize its wealth management business. Morgan Stanley’s trading businesses are underperforming, so it is even more dependent on wealth management.

If Perella Weinberg attaches a value on the low side, close to $9 billion, analysts say it could lead Morgan Stanley shareholders to have doubts about the wealth management business, too.